A comparative essay asks that you compare at least two (possibly more) items. These items will differ depending on the assignment. You might be asked to compare:
Although the assignment may say “compare,” the assumption is that you will consider both the similarities and differences; in other words, you will compare and contrast.
From "The comparative essay", Vikki Visvis & Jerry Plotnick, in Writing Advice, University of Toronto, accessed 5/06/2017, <http://advice.writing.utoronto.ca/types-of-writing/comparative-essay/>
A literary comparison essay is an essay that examines two or more works in relation to one another. It examines a select set of similarities and differences. When reading for analysis, you are not reading for a surface understanding, you are reading to understand why things happen and what the deeper meaning behind a character is, or a setting, or an event.
To deconstruct the topic thoroughly: rewrite the topic in your own words; ask questions of the topic; brainstorm ideas, list your key points in order to ensure that you do not ignore any key element of the topic. Consider which quotations and/or specific text references you can draw on to illustrate and illuminate your key points. Order your points to allow for a logical and cohesive discussion and ensure that you have selected enough examples and quotations for each text to enable sufficient comparison to unfold.